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Books - Science - Mathematics - Mathematical Analysis - For the Aspiring Analyst

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Elementary Classical Analysis
by Jerrold E. Marsden, Michael J. Hoffman
Average Customer Review: 3.5 out of 5 stars
Hardcover (15 March, 1993)
list price: $108.95 -- our price: $108.95
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Reviews (9)

3-0 out of 5 stars Don't see why its used in so many classrooms
I am currently taking a course in analysis, and our instructor is using this book as his primary teaching material. I have to say that I am not impressed with this book at all. There are parts where the author goes to great lengths explaining things that seem may evident (to me at least) for any student familiar with calculus, and then there are times I feel helplessly lost in his lack of explanation. The only positive thing about this book is its excercises and problems, they are placed strategically in the book, meaning that the easier problems and the hard ones are placed in the book appropriately. The easy problems inject confidence for beginners while the tougher ones will, no doubt, challenge even the most confident students.

2-0 out of 5 stars Not So Hot.
Unevenly written. Full of typos. Some sections, like the one describing types of matrices, are so incompetently worded as to defy complete comprehension, even with repeated readings. Although some of the coverage of topological material is good, overall the informal explanations don't really do much to supplement the rigorous proofs -- they're just sort of... verbose. Not recommended. (Instead, try "Yet Another Introduction to Analysis" by Victor Bryant, as a fine introduction to the subject.)

5-0 out of 5 stars An excellent introduction to Real Analysis
Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:

"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."

Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.

A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view. ... Read more

Isbn: 0716721058
Sales Rank: 371655
Subjects:  1. Mathematical Analysis    2. Mathematics    3. Reference    4. Mathematics / General   


$108.95

Elementary Real and Complex Analysis (Dover Books on Mathematics)
by Georgi E. Shilov, Richard A. Silverman
Average Customer Review: 4.5 out of 5 stars
Paperback (01 February, 1996)
list price: $19.95 -- our price: $13.57
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Reviews (6)

5-0 out of 5 stars Getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

3-0 out of 5 stars Possibly too simple
As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin.

5-0 out of 5 stars A wonderful text -- Highly recommended!
I purchased this book as a reference book for my first analysis course.It is very well written, and easy to follow.Dr. Shilov has a very nice way of organizing this text:He puts all the definitions at the beginning of the chapter and the subsequent sections are results of those definitions.It makes for a very quick reference.His presentation of the included proofs is also very nice.There were several occasions I found myself thumbing through it for a second perspecitve.

As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology.He does keep in mind this is intended for undergrads and first year grads though.

Oh, another nice feature is the price!I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course. ... Read more

Isbn: 0486689220
Sales Rank: 120397
Subjects:  1. Calculus    2. Mathematical analysis    3. Mathematics    4. Science/Mathematics   


$13.57

Mathematical Analysis (2nd Edition)
by Tom M. Apostol
Average Customer Review: 4.5 out of 5 stars
Paperback (01 January, 1974)
list price: $119.40 -- our price: $119.40
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Reviews (15)

5-0 out of 5 stars One of the best I own...
I own books on mathematical analysis by Browder (0387946144), Douglas S Bridges (0387982396
), Haaser Sullivan (0486665097), Pfaffenberger(0486421740), Dudley (0521007542),Abbot(0387950605) and Apostol.

All books cover abstract multivariable spaces, except Abbott who limits himself to the real line.
None of these books are perfect, but of all these books Apostol is the one I prefer for the following reasons :

1. The contents :I think a beginning analysis course should serve two aims :
a. teach basic techniques that can be used in other theoretical oriented courses like physics,economics,...
b. at the same time let the students discover the beauty of abstract and rigorous math.

In this context Apostol has reached the ideal mix between abstraction and usability. He covers practical topics , used as a basis in a lot of other courses, but he does this by making the needed level of abstraction in order to proof everything in a rigorous way.

Each book is self contained, though none of these books give a good introduction into basic mathematical logic. However an introduction to set theory is explained well in all books.
Dudley 's beautifull book is the most abstract but requires the highest level of mathematical maturity.

2 Layout : The books of Haaser Sullivan , Pfaffenberger cover excellent material in a very clear way but they are cheap Dover editions, putting as much text as possible on one page. Browder 's contents I like most (and contains really excellent explanations), but his layout is also very dense and not always comfortable to read. The layout of Apostol is the best of all these books, its pages are well filled, but the difficult proofs contain enough whitspace for a confortable read.

3.Completeness and rigor : Apostol and all these books, except Abbott and Douglas S Bridges, proof everything they mention (exceptionally, they leaf a proof as an exercise, but then the proof is relatively easy enough if you understand the material). This is an approach I like : present the complete theory and then (like all of them do) create challenging exercises seperate from the basic theory.
In contrast, the book of Douglas S Bridges represents all material as one big exercise.This is nice if you have anough time, but most of us do not have that much time,I am afraid. Also Abbott has a lot of difficult proofs left as an exercise to the reader. But at the same time, Abbott is the best in motivating the reader. Abbott often provides excellent background in order to motivate the reader and sharpen the readers mathematical intuition.

While Apostol is not best on all the criteria mentioned above, Apostol scores good on all off them and as a consequence he has the best total average. This being said, I must omit that reading Apostol requires patience. Yes his explanations are clear, but can be very terse (especially his examples). Though, in principle everything is explained without gaps. This book requires reading every word carefully and take the time to reflect, but maybe that is the only way to learn advanced math.

Finally a remark about the price, I bought this book in Europe where it is much cheaper (check amazon.co.uk)

So compared with the others this a very good book.

5-0 out of 5 stars The Cat's Meow
As stated by prior reveiwers, this books does assume that the reader is Mathematically mature (a saying most young Mathematicians despise), in the sense that he/she must be able to follow the logical development of any given arguement, be able to 'see' where and how topics are related as well as fill in any blanks that may present themsevles in a given definition/proof.Apostol, as compared to Rudin, does a nice job of filling in these blanks by adequately providing all of the necessary details within a proof.This book will provide the willing student with a solid foundation in elementary analysis as well as the confidence to persue higher analysis.The only draw back to Apostols book, aside from cost, is that the constant Theorem - Proof - Theorem format can be overwhelming at times and cause some readers to cover material too quickly.Despite the book's cost I would highly recommend this book over "baby" Rudin (that is, Principles of Mathematical Analysis) since Rudin is notorious for not filling in the blanks within a given proof and instead provides seemingly 'slick proofs'.

5-0 out of 5 stars A cut above the rest...
I am currently studying from Apostol's book, completeing a year-long course with his treatment of the Lebesgue integral. While my experience with comperable analysis texts is not exhaustive, I am familiar with the more notable: "Baby" Rudin, Marsden,... So, I can confidently say that Apostol's text is among best covering the subject. His treatment is well modivated with examples, and his proofs, while not as not as "elegant" as those of Rudin, are surely more pedagogical in nature. Apostol has included a large amount of exercises that range througout the gamut of difficulty, and the material is peppered with a treatment of complex varaibles. Also, the readability is something to be attained by all authors of mathematics texts.

One drawback to the text is a too abstract approach to the Implict and Inverse Function Theorems. I found these to be the most challenging in the text, and I was forced to return to my copy of Stewart's Calculus text to re-acquiant myself with each concept. Also, at times Apostol falls into the pattern of Definition, Theorem, Definition, Theorem,..., but this seems to be only in the cases when ample preparation is needed to provide noteworthy examples; eg. Lebesgue integration.

So, in spite of the cost, I highly recommend this text for the study of real analysis (even for self study), although at [this price] there are bound to be others that have a higher value to cost ratio. Having completed the text (almost), I feel prepared to begin a more abstract study of analysis. ... Read more

Isbn: 0201002884
Sales Rank: 338513
Subjects:  1. General    2. Mathematical analysis    3. Mathematics   


$119.40

Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics)
by WalterRudin
Average Customer Review: 4.5 out of 5 stars
Hardcover (01 January, 1976)
list price: $138.13 -- our price: $138.13
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Reviews (73)

5-0 out of 5 stars An excellent textbook
I think mathematics is a part of our culture.That's why, as a non-math major, I wandered into a very serious analysis class for mathematics majors.That might have been a disaster for me.Luckily, we used this book as a text, and it saved me.I read the whole book and diligently did all the exercises (of course, back then, it was the first edition, with only 227 pages and 140 exercises; it's somewhat more now).And that is my recommendation today.Read the book carefully and do as many exercises as you can.It certainly isn't easy.But it isn't, um, countably hard either.

The material in the book is self-contained.I guess that in theory, it could be mastered by any bright 14-year old who had learned some high school algebra and geometry.But I would surely recommend having much more mathematical sophistication than that as a prerequisite!

If you haven't learned the language of mathematics before, you'll enjoy the use of terms such as "countable," "real," "rational cuts," "measure," "ring," and "complete." By the end of the book, when the author claims that a proof (involving Cauchy sequences no less) is complete, you'll barely be able to suppress a desire to ask "Does every Cauchy sequence in the proof converge?"

In the first edition of this book, Rudin did mess up a little in his section on "the integral as a limit of sums." His theorem as stated was false.We cruelly dubbed it "Rudin's Last Theorem."Worse, he had used it "to prove some elementary properties of the Stieltjes integral."But that was all straightened out by the second edition.

I especially like the first couple of chapters.They give most readers the confidence to continue.And the final chapter, on Lebesgue integration, is very well written.One note of warning, though.Rudin begins this chapter by saying, "Some of the easier propositions are stated without proof.However the reader who has become familiar with the techniques used in the preceding chapters will certainly find no difficulty in supplying the missing steps."That is an exaggeration.It takes work.After all, this is, um, real mathematics you'll be doing!

I'm thankful that I was assigned this as my textbook.

5-0 out of 5 stars A masterpiece
I absolutely agree with Professor Jorgensen.

I loved it when I was a student of physics, and I still love it because I tend to consider it as my personal standard in Classical Mathematical Analysis (and not only): sort of a "pacemaker" which sets the qualitative level to go back to just every time one is a little confused about what to do and where to go ;)

4-0 out of 5 stars Great analysis...
This book is tough to learn from (because it has almost no motivation), but the text is clearly written and easy to understand.

The proofs are elegant and easy to follow.The construction of the reals using dedikind cuts along the rationals is the only construction I've found in introductory books.Other books I used as suplementary to this (Rosenlicht and Bear) did not have this in their texts.

After learning analysis, I find this book to be an excellent reference for anything that I might have forgotten or just didn't understand the first time around. ... Read more

Isbn: 007054235X
Sales Rank: 29749
Subjects:  1. Advanced    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Advanced   


$138.13

Topology (2nd Edition)
by James Munkres
Average Customer Review: 5.0 out of 5 stars
Hardcover (28 December, 1999)
list price: $106.67 -- our price: $106.67
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Reviews (24)

5-0 out of 5 stars The best rigorous introduction to general topology!
I have owned the 1975's first edition (red cover) of this book which I am currently studying again to pass a Ph.D. qualifying exam on topology. From the many topology texts that I have come across over the years, this one easily stands out as the best rigorous introduction to point set topology for a beginning graduate student. It covers all the standard material for a first course in general topology beginning with a chapter on set theory, and now in the second edition includes a rather extensive treatment of the elemantary algebraic topology. The style of writing is student-friendly, the topics are nicely motivated, (counter-)examples are given where they are needed, many diagrams provided, the chapter exercisesrelevant with the correct degree of difficulty, and there are virtually no typos.

The 2nd edition fine tunes the exposition throughout, including a better paragraph formatting of the material and also greatly expands on the treatment of algebraic topology, making up for 14 total chapters (as opposed to 8 in the first edition). A notable minor issue in the first edition was the consistent usage of the pronoun "he" in the discussions for addressing all the possible readers of the book. (This fortunately has been modified in the 2000's edition.) On another note, I wish there were some hints & answers provided at the back of the book to some of the harder problems, so as to make this text more helpful for those of us who use it for self-study.

One of the two spotlight reviewers has correctly mentioned that Munkres does not cover differential topology here. I speculate this is perhaps because Munkres has already a separate monograph on differential topology. It is also necessary to get a handle on some fair amount of algebraic topology first, for a full-fledged coverage of the differential treatment. Regardless, one great reference for a rigorous and worthwhile excursion into differnetial topology (covering also Morse Theory) is the excellent monograph by Morris W. Hirsch, which is available on the Springer-Verlag GTM series.

At the end, I shall mention that one other very decent book on general topology which has unfortunately been out of print for quite some time is a treatise by "James Dugundji" (Prentice Hall, 1965). The latter would nicely complement Munkres (for example, Dugundji discusses ultrafilters and some more of the analytic directions of the subject.) It's a real pity that the Dover publications for example, has not yet published Dugundji in the form of one of their paperbacks.

5-0 out of 5 stars great!
Not much to add here... there are enough easy problems that I can get the hang of something, but also some really tough ones at the end of each problem section. The proofs and examples in the text are really good guides to doing the problems also. In some sections there are counterexamples for, say, the converse of a theorem which are always really pathological. At the beginning of each section there is some discussion on what to expect, why the stuff is important, what to do with it, etc. Even though I had a really good prof for the topology course I did this book was very helpful out of the classroom.

5-0 out of 5 stars Excellent Topology Book
My introduction to Munkres was in an independent study of point set topology in my final semester of undergraduate work. A professor assigned me problems from the book, but my learning was largely self motivated.I found that it was an excellent book for independent study.The text was clear and readable and the exercises helped to cement the concepts that are introduced in the reading.

Later at graduate school, Munkres was also used in a topology class at the beginning graduate level.Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book.Sometimes I had difficulty following exactly what the professor was doing at the blackboard, but I could always understand what was going on when I consulted Munkres.

I would stress that this is only to be used as an introduction to algebraic topology, as there is nearly no development of homology groups and other algebraic concepts.However, it gives a very good presentation for the fundamental group.As a whole it would be a very good addition to your mathematical library. ... Read more

Isbn: 0131816292
Sales Rank: 76455
Subjects:  1. Algebra - General    2. Mathematics    3. Science/Mathematics    4. Topology    5. Topology - General    6. Mathematics / Algebra / General   


$106.67

The Way of Analysis (Jones and Bartlett Books in Mathematics)
by Robert S. Strichartz
Average Customer Review: 4.0 out of 5 stars
Paperback (01 June, 2000)
list price: $86.95 -- our price: $86.95
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Reviews (16)

4-0 out of 5 stars Lots of description... a bit too much
The book is excellent for self-study with its in-depth descriptions.The reader should look out for the occasional misprint (even in definitions, which makes it a bit more difficult), but if the book is read carefully these errors expose themselves.The reader should highlight definitions for later reference (since they are sometimes within the text).

In use for a class or for reference, this book is too wordy.Definitions are difficult to spot in many cases (some are written directly within the text).Descriptions also drag on too long in many cases, making it difficult to read the entire text.The book is by no means concise, which, after sitting in a lecture on the topic, makes much of the description too repetitive.

The problems the book offers are very good, in that they require thought but are also possible for someone fairly new to analysis (although this isn't unique to this book).The proofs are clear and many are quite elegant.They need no explanation other than what is in the text (how it should be).

One last comment on the book itself -- this book is too big to be a paperback and hold up under typical use.Look for this one in a hardcover edition, if you can find one.

Recommended instead of this book: "Principles of Mathematical Analysis," by Walter Rudin.This book is concise and clear and most appropriate when taken with a course, but must involve careful reading for self-study in comparison of Strichartz's book.

5-0 out of 5 stars Very lucid and ideal material for learning real analysis
Most books on mathematics simply dump concepts,equations and examples and let you figure out what to do. Not this one. The book is written in a passionate manner where the author takes pains to explain why we are going in a particular direction and the goals. The style is extremely lucid and informal, something unusual for a subject that is steeped in formal mathematics. Yet the author presents, explains and covers all the formal theorems, concepts etc . The book also has excellent exercises. A truly noteworthy achievement. I would highly recommend this to anyone (especially self-study) trying to learn this subject.

5-0 out of 5 stars The best to understand and do Analysis
This is the best Analysis book I ever read, you can learn not only the subject, but how to do Math, the introductive paragraph in each chapter gives the motivation of the topic, for example the introduction to the Lebesgue integral is memorable, many people "learn" the Lebesgue theory passively, some think it is a play to integrate strange functions, instead Prof. Strichartz treats estensively the PRACTICAL weaknesses of the Riemann theory.
For important theorems it is underlined the importance of every hypotheses, often from many points of view, the errors of the past are cited, I think one can learn more from explanations and errors than from a crystallized theory.
The notation is not standard and the printing is not good, however these are light faults. ... Read more

Isbn: 0763714976
Sales Rank: 335098
Subjects:  1. Calculus    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics   


$86.95

Undergraduate Analysis (Undergraduate Texts in Mathematics)
by Serge Lang
Average Customer Review: 4.0 out of 5 stars
Hardcover (May, 2005)
list price: $69.95 -- our price: $59.48
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Reviews (4)

4-0 out of 5 stars Just like every other Lang text
This book typifies Lang's style. If you enjoyed any of his other books you'll enjoy this too. Like seemingly all of his texts, it has a section on the inverse function theorem and makes quite a deal out of it. Overall, it is quite comprehensive, but there's little motivation for the proofs so things can be a bit boring. Both Rudin and Browder cover the same amout of material in far fewer pages, and they have better excerises too.

5-0 out of 5 stars Solid, complete reference to basic analysis topics
Serge Lang's "Undergraduate Analysis" offers an impeccable selection of topics and exercises for the student wishing to broaden his/her knowledge of analysis. The proofs of theorems can be terse at times, but a hardworking student will gain much through a thorough reading of the text. Also, Lang concentrates many of his exercises on estimates, which is an art form that is slowly dying among undergraduates (and graduate students as well, sad to say). Many of his problems require only the triangle inequality (the basic tool of estimation) and ingenuity (and hard work) from the student. I would strongly recommend this text for anyone who wishes to fully understand and appreciate the results and techniques of basic real analysis.

2-0 out of 5 stars okay
I personally don't care much for this book.It's too terse, and there are nowhere near enough examples.I have about 6 analysis books and this is the one I look in the least.It seems to cover a lot of stuff, but maybe too much-- it wouldve been better to focus more on some more elementary topics.For instance, he spends about one and a half pages introducing the derivative.So if you want a book that glosses over more elementary concepts and leans heavily toward a graduate level, this book's for you.At my school we were supposed to learn advanced calculus from this and it is not good for that at all.For advanced calc try robert stritchart's Way of Analysis (the best book on analysis I've ever read) and for analysis Intro to real analysis by kolmogrov (only 10 bucks or so and actually better than most books costing a 100) ... Read more

Isbn: 0387948414
Sales Rank: 421698
Subjects:  1. Calculus    2. Education    3. Mathematical Analysis    4. Mathematics    5. Analysis    6. Differentialrechnung    7. Integralrechnung    8. Mathematics / Mathematical Analysis   


$59.48

Principles of Real Analysis
by Charalambos D. Aliprantis, Owen Burkinshaw
Average Customer Review: 4.0 out of 5 stars
Hardcover (15 September, 1998)
list price: $98.95 -- our price: $98.95
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Reviews (3)

5-0 out of 5 stars Excellent Coverage plus a wealth of problems
Finished reading those undergraduate analysis books that made a study of metric spaces look like a tall order? Well then reading this book would be an excellent continuation of the hard work. The book is largely about the Lebesgue theory of integration, but includes a very thorough coverage of the theory of metric and topological spaces in the first two chapters. Chapters 3,4 and 5 are the heart of the book covering measure theory, the Lebesgue integral and some topics from introductory functional analysis like theory of operators and Banach spaces. Chapters 6 and 7, covering Hibert spaces, the Radon Nikodym theorem and the Riesz Representation Theorem among other things, are the most useful for someone like me who wants to master higher analysis in order to read financial mathematics. And what's more, there is a solutions book providing answers to all 609 problems (spread over 7 chapters!) and more. All in all, the authors have made a great contribution!

2-0 out of 5 stars Very Mediocre Contents, Terrible Aesthetics
I was very disappointed in this book and judging from the steady decline of the resale price here on amazon.com, I can see others agree.

First of all the book looks like it was photocopied in someone's basement - the text is completely faded out and paper feels terrible. For almost $100, I expect a little more.

The actual contents of the book are not much better. I found Royden (the required text for our class) to be very sparse and was hoping for something to fill in the details. This book did little to help. It covers integration in a rather idiosyncratic way, devotes little time to differentiation, and says nothing about convexity.

If you are looking for a good anaysis book I recommend either "Lebesgue Integration on Euclidean Space" by Frank Jones or the slightly more abstract "Real and Functional Analysis" by Serge Lange

5-0 out of 5 stars One of the best
An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text. ... Read more

Isbn: 0120502577
Sales Rank: 445964
Subjects:  1. Differential Equations    2. Functions Of Real Variables    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / Mathematical Analysis   


$98.95

Real Analysis (3rd Edition)
by Halsey Royden
Average Customer Review: 3.5 out of 5 stars
Hardcover (02 February, 1988)
list price: $114.67 -- our price: $114.67
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Reviews (17)

4-0 out of 5 stars Standard Analysis Text; Necessary, but not Sufficient!
Very useful textbook, easy to follow.
A little over-simplified though.
Doesnot leave a lot of gaps, but then that doesnot leave a lot of room for imagination either.
At times it gets toooo wordy, if you know what I mean. Less ideas and more talk.
A stark contrast to Rudin, but can be very useful if both are used together. However, if you need to choose between those two, go with Rudin.

5-0 out of 5 stars this book is just plain good.
I began as a graduate student in applied maths less than a year ago; all of the students that I spoke with prior to that said that real analysis with rudin's book was their worse & hardest class..
So when I walked into MTH 5111 Real Variables I thought oh *&^% what am I in for?? but then I picked up the Royden book and I understood the way he was presenting the materail.. the book is very stright to the point + leaves channelgning problems to the HW sets but the autor clearly outlines. I have learned more from this book and course than any other...

4-0 out of 5 stars Not bad for self-study, excellent for reference
I used Royden (2nd edition) as a graduate student over 30 years ago, and have been away from real analysis pretty much ever since (not because of the book(!), but because of being in computers).I've taken a renewed interest in the subject (I'm a pretty random person) and have been surprised at how the material has come back to me, I think because of the readability of the text.It's true, Royden challenges the reader at every turn, but if one has acquired the level of mathematical maturity commensurate with strong interest in analysis, the challenges are appropriate, in my opinion ... Read more

Isbn: 0024041513
Sales Rank: 147851
Subjects:  1. Advanced    2. Functional Analysis    3. Functions Of Real Variables    4. Mathematical Analysis    5. Mathematics    6. Measure theory    7. Science/Mathematics    8. Mathematics / Advanced   


$114.67

Real and Complex Analysis (Higher Mathematics Series)
by WalterRudin
Average Customer Review: 4.5 out of 5 stars
Hardcover (01 May, 1986)
list price: $140.94 -- our price: $140.94
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Reviews (16)

5-0 out of 5 stars A start in math.
I am a fan of Rudin's books. This one "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world.

The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.

I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.

What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.

Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.

After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"

Review by Palle Jorgensen, September 2004.

5-0 out of 5 stars Welcome to the self-service analysis center!
This year we have been using Walter Rudin's treatise as the main text for a standard first-year graduate sequence on real analysis, backed up by Wheeden/Zygmund's book on Measure and Integral, and the two seem to complement each other quite nicely. Rudin writes in a very user-friendly yet concise manner, and at the same time he masterfully manages to maintain the high level of formality required from a graduate mathematics text. To be totally honest, a few years ago my very first attempt at learning graduate-level real analysis in a classroom setting (via Folland's book) was not successful, as I found the exposition in Folland very dense and rigid, and the homework problems too difficult to do. Rudin's book however is a lot more accessible for the beginning graduate students who may not have had any more than some basic exposure to measure theory in their upper division analysis classes. One point to keep in mind is that Rudin developes the measure in the more formal axiomatic way, instead of in the more concrete constructive approach. In the constructive approach, one first introduces the "subadditive" outer measure as a set function which is defined on the power set P(X) of a nonempty set X. One then proceeds by showing that the restriction of the domain of the outer measure to a smaller class of subsets of X (a sigma algebra M), obtained via applying the Caratheodory's criterion, results in a "countably additive" set function which is called a measure on (X,M). (The latter is the approach taken in both H.L. Royden and Wheden/Zygmund). The formal approach is not very intuitive and is less natural for a beginning graduate student who might not have developed a certain level of mathematical maturity yet.

Also, Rudin does not discuss some of the more advanced or interdisciplinary topics such as distribution theory (Sobolev spaces, weak derivatives, etc.) or applications of measure theory to the probability theory, both explored in the book by Folland. Last but not least, it's worth noting that contrary to the common practice, Folland includes many end-of-chapter notes where he outlines some important historical aspects of the development of the topics, and also gives a few references for further study. For example, in the notes section at the end of the chapter on Lebesgue integration, he mentions --and briefly outlines-- the basics of the theory of "gauge integration" (also called Henstock-Kurzweil theory) which serves to construct a more powerful integral than that of the Lebesgue's. As another instance, having already defined and used "nets" within the chapter on topology, in the end-notes Folland also introduces "filters" and "ultrafilters". These are all machineries which have been developed to play the role of the metric space sequences in general (locally Hausdorff) topological spaces, but for some historical reasons, ultrafilters have nowadays taken a backseat to the nets (the older general topology books usually prove the Tychonoff theorem using ultrafilters). All said, I can recommend taking up Royden as your very first approach to measure theory, then based on how well you think you have learned the first course, move on to either Rudin or Folland for a more advanced treatment. Please note that the other books I have mentioned above do not discuss complex analysis, a subject which is also masterfully presented in Rudin. There are however a few other equally well-written complex analysis books to pick from, for example John B. Conway's classic from the Springer-Verlag graduate series, or L.V. Ahlfors' masterpiece, to name just a couple.

5-0 out of 5 stars A Comprehensive Guide to Analysis
Rudin's Real and Complex Analysis is an excellent book for several reasons.Most importantly, it manages to encompass a whole range of mathematics in one reasonably-sized volume.Furthermore, its problems are not mere extensions of the proofs given in the text or trivial applications of the results- many of the results are alternate proofs to major theorems or different theorems not proved.With that in mind, this book is not appropriate for a course where the instructor wants students to merely understand the theorems well enough to develop applications- the structure of the book is far better suited for a more theoretical course.

For example, the construction of Lebesgue measure is considered one of the most important topics in graduate analysis courses.After this construction, more abstract measures are developed, and then one proves the Riesz Representation Theorem for positive functionals later.

Conversely, Rudin develops a few basic topological tools, such as Urysohn's Theorem and a finite partition of unity, to construct the Radon measure needed in a sweeping proof of Riesz's Theorem.From this, results about regularity follow clearly, and the construction of Lebesgue measure involves little more than a routine check of its invariance properties.

Another example of where Rudin takes a more theoretical approach to provide a more elegant, yet less intuitive proof, is the Lebesgue-Radon-Nikodym theorem.Other books generally introduce signed measures with several examples, and use this result, along with properties of measures to derive the proof.On the other hand, since the first half of the book contains an intermission on Hilbert Space, Rudin uses the completeless of L^2 and the Riesz Representation Theorem for a more sweeping proof.

In the real analysis section, Rudin covers advanced topics generally not covered in a first course on measure theory.The chapters on differentiation and Fourier analysis are key examples of this.Rudin uses maximal functions to develop the Lebesgue Point theorem and results from complex analysis, and provides an incredibly thorough proof of the change-of-variables theorem.The ninth chapter, on Fourier transforms, relies heavily on convolutions, which are developed as a product of Fubini's theorem.This, in turn, is used to prove Plancherel's theorem and the uniqueness of Fourier transforms as a character homomorphism.

The tenth chapter, on basic complex analysis, essentially covers an entire undergraduate course on the subject, with added results based on a solid knowledge of topology on the plane.Once a solid foundation on the topic is laid, Rudin can develop more advanced topics from Harmonic analysis using general results from real analysis like the Hahn-Banach theorem and the Lebesgue Point theorem (for Poisson integrals).

Most of the basic results from the power series perspective are covered in the text, but while the geometric view is examined, it is still done in a very analytic, formula-based way that does not allow the reader to gain too much intuition.Nonetheless, all the basic results are covered, and Rudin uses these to develop the main theorems, such as the Mittag-Leffler and Weierstrass theorems on meromorphic functions, and the Monodromy Theorem and a modular function used to prove Picard's Little Theorem.

As an introductory text, even for advanced students, Rudin should probably be accompanied by more descriptive texts to develop better intuition.In fact, I would recommend Folland's Real Analysis and Ahlfors' Complex Analysis for self-study, because the problems are easier and one can learn better through those.With a good instructor, though, Rudin's text is concise and elegant enough to be both useful and enjoyable.It is also a good test to see how well one REALLY knows the subject. ... Read more

Isbn: 0070542341
Sales Rank: 196045
Subjects:  1. Advanced    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Advanced   


$140.94

Basic Complex Analysis
by Jerrold E. Marsden, Michael J. Hoffman
Average Customer Review: 4.0 out of 5 stars
Hardcover (15 December, 1998)
list price: $108.95 -- our price: $119.49
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Reviews (12)

3-0 out of 5 stars Quite Dry
This is the second book that I have read beside the Vector Calculus by Marsden and Hoffman.This book rushes you through with an introductory chapter and go right into the heart of complex analysis.The author assumes you to have a great professors that can explain things in detail when you can't quite understand what is written in the text.Unfortunately I did not have a great instructor.

The examples of the book are quite simple, compare to some end of section problems.

Overall this book has no surprises as it is quite dry, got bored from reading it.If it was not a required text book for a 3rd year complex analysis course, i wouldn't recommend it to anyone.There are many other books out there that are better written.

5-0 out of 5 stars A versatile introduction to the subject.
I used an earlier edition of this text as an instructor 20 years ago.The students in my class at the time were equally divided among the fields of mathematics, physics, and engineering.The book proved to be quite useful for all of them.Marsden skillfully strikes a balance between the needs of math majors preparing for graduate study and the needs of physics and engineering students seeking applications of complex analysis.

The book is clearly written and well-organized, with plenty of examples and exercises.My only significant criticism of the first edition was the author's tendency to label many examples of contour integration as theorems.Technically, there is nothing wrong this, but I found that some of my students tended to memorize the statements of these "theorems" rather than focus on the methods of integration discussed (for example, "Pac-Man" integrals with branch cuts along rays other than the positive real axis).Nonetheless, this is a fine text that has--not surprisingly--continued to be widely used for over two decades.

3-0 out of 5 stars Mediocre Textbook!
Complex analysis is a simple subject to teach and to learn. There is no reason to include so many pages, still couldn't comprehensively cover all the salient points. Mediocre students taught by mediocre teachers will byall means find this book "excellent" in their own right! Idisagree with both one-star and five-star rating. I did find my studentsconfused by this book and its "answers". It is notstudent-friendly at it worst. I will never use this book as my textbookagain despite my distaste of its price tag. Unfortunately, the math levelof US college students is persistently sliding down. The level of reviewingthis book as well as many others are also disappointingly low. For UScommunity college complex analysis course, this book can be rated for fivestars. But, for major universities such as U. C. Berkeley, MIT and Caltech,this book deserves a three-star rating fairly. After all, there are good USuniversities ranked high in math level among the world. ... Read more

Isbn: 071672877X
Sales Rank: 477884
Subjects:  1. Functions Of Complex Variables    2. General    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Complex analysis    7. Mathematics / General   


$119.49

Complex Analysis (Graduate Texts in Mathematics)
by Serge Lang
Average Customer Review: 4.5 out of 5 stars
Hardcover (15 January, 1999)
list price: $69.95 -- our price: $59.83
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Reviews (4)

5-0 out of 5 stars sweet dude
I dont like lang's algebra, ugrad linear algebra, or diff/riemannian manifolds books all that much, but i LOVED this one.

I think an undergrad with calculus and patience can read it.
there are characteristic lang-style things like research-oriented material, and he actually has examples. He covers topics towards the end of the book which arent common elsewhere, so i've never put it down. I am not a mathematician and I like this book. It's in one of my standard 8 books that I dont leave home without (4 physics 4 math)

3-0 out of 5 stars A good book, but not for beginners.
if you want an introduction to complex analysis, I advise you to pass onthis book, and read Churchill and Brown's introductory book. Having saidthis, part I of Lang's book will seem mostly review if you follow myadvice. Part II, on Geometric Function Theory, is more advance materialthat is presented reasonably well.

4-0 out of 5 stars Not TOO complex
A person with absolutely no knowledge of complex numbers couldbegin with page one of this book.However, I think that some exposure to analysis is helpful before finishing the first chapter, but not necessary.I foundthis book easier to read & understand than some real analysis books,yet it helped me further understand real analysis in the process.I'm surethis is due to mere repetition of some of those concepts over a differentfield.As the author mentions in his foreword, the first half of the bookcan be used as an undergraduate text (Jr/Sn years) and the second half canalso, but I would NOT have enjoyed it in undergraduate studies.I found itworthy of a first course in complex numbers at the graduate level.Iespecially liked it after studying real numbers.The placement of thechapter subject matter can be altered (to some degree) to ones liking.Ithink Lang has provided good examples & problems.There's a solutionsmanual (by Rami Shakarchi) for this text somewhere.

A brief discriptionof the chapters (some of them at least):

Chp 1:basic definitions &operations, polar form, functions, limits, compact sets, differentiation,Cauchy-Riemann eqs, angles under holomorphic ("differentiable")maps.

Chp 2:formal & convergent power series, analytic functions,inverse & open mapping thms., local maximum modulus principle

Chp 3: connected sets, integrals over paths, primitives("antiderivatives"), local Cauchy thm, etc

Chp 4:windingnumbers, global Cauchy Thm, Artin's proof

Chp 5:Applications ofCauchy's integral formula, Laurent series

Chp 6:Calculus of residues,evaluation of complex definate integrals, Fourier transforms, etc(funstuff)

Chp 7: Comformal mapping, Schwarz lemma, analytic automorphisms ofthe Disc

Chp 8:Harmonic functions; Chp 9: Schwarz reflection; Chp 10: Riemann mapping theorem; (11):Analytic continuation along curves; (12)applications of Maximum Modulus Principle an Jensen's Formula; (13)Entire& Meromorphic functions; (14) elliptic functions; (15) Gamma & Zetafunctions; (16) The Prime Number Theorem; and a handy appendix. ... Read more

Isbn: 0387985921
Sales Rank: 263854
Subjects:  1. Functions Of Complex Variables    2. Mathematical Analysis    3. Mathematics    4. Probability & Statistics - General    5. Science/Mathematics    6. Mathematics / Mathematical Analysis   


$59.83

Beginning Functional Analysis
by Karen Saxe
Average Customer Review: 3.5 out of 5 stars
Hardcover (07 December, 2001)
list price: $44.95 -- our price: $44.95
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Reviews (4)

2-0 out of 5 stars I'm Sorry
I'm sorry I had to read this book, I'm sorry anyone else had to read this book, and I hope that no one else has to suffer through this book.Pedagogically speaking, it is un-sound to state, in the first chapter and in the first several pages, a theorem and, rather than set a tone and rhytmn for the book, good 'ole Saxes leaves these theorems to the reader as exercises.Now, Saxe is not Lang and the Springer book series, namely, undergraduate texts, is just that, for undergraduates, for young students, mathematically speaking, and hence such an adverse and lazy tone should not be set in such a book.Furthermore, her direction, her flow, her in-ability to illuminate and bring forth the beauty of Functional Analysis is depressing (see Ascoli's Theorem and, while your seeing things, maybe Saxes should have seen an editor).For those of you who have had some Analysis, are familiar with basic point-set topology, and have a general idea of what it means for a mapping between to spaces to be linear, then the book you should read is that of Erwin Kreyszig.This book provides you with all the necessary tools as well as motivated and complementary exercises (some solutions are provided).Steer far away from Saxe's book.As an aside, it is obvious that no book, and hence no author, is perfect or capable of producing a 'perfect' book.The problem that arises in the case of the current book being reviewed is that considerable knowledge and or passion for a given subject does not necessarily imply that you are capable of re-casting this knowledge in the form of a book.Maybe, just maybe, if there is a future reprint, hopefully, Saxe will be able to re-work the book and create something hjigher in quality.Until that time, go else-where if you are interested inl earning Functional Analyiss.

1-0 out of 5 stars Quite a bad book.
A lot of bla bla in this book. This book is a collection of noteswithout a guideline in mind. The more interesting subjects of functional analysis are only superficially treated. Proofs are often quite shortly illustrated and in a proof I found a gigantic error. Not worth to buy this book.

5-0 out of 5 stars Lucid
This book is fantastic! It is an extremely readable account of the basics of the subject. I thought the Chapter on Measure Theory and Lebesgue integration were particularly well organized. Every definition was well motivated and the theorems were arranged in a very natural progression.

One thing I especially enjoyed about this book is that most of the proofs are done only for special cases of theorems, without loss of generality. For example, the Arzela-Ascoli theorem is proved for the function space C([a,b],R) (R = real numbers), but then Saxe points out what makes the proof 'tick' so that the reader may easily modify it to a more general setting (she always states the more precise versions of such theorems as well). This is great because it helps one's intuition without getting short-changed.

Finally, the book has a great wealth of historical notes and biographies which are rich in mathematical content (e.g., Saxe explains that Frechet was the first person to define a metric space even though he called it 'une class E'; Hausdorff gave it its modern name in 1914). The reader can in this way appreciate how the subject slowly developed into its present form.

This book is a jewel! I myself am not the biggest fan of functional analysis, but this book made me really appreciate the subject. ... Read more

Isbn: 0387952241
Sales Rank: 710778
Subjects:  1. Combinatorics    2. Functional Analysis    3. Mathematics    4. Probability & Statistics - General    5. Science/Mathematics    6. Mathematics / Mathematical Analysis   


$44.95

Introductory Functional Analysis with Applications
by ErwinKreyszig
Average Customer Review: 5.0 out of 5 stars
Paperback (23 February, 1989)
list price: $71.95 -- our price: $71.95
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Reviews (7)

5-0 out of 5 stars The best undergraduate introduction to the subject
I can't think of a better place to begin learning functional analysis. The book is ideally suited for undergraduates or beginning graduates who have had one or two semesters of real analysis, linear algebra, and possibly topology. The author seemed extremely lucid with clear worked out examples. Phrases like "it's obvious" or "it should be clear" were not so frequent. It's quite a beautiful subject, with the last chapter providing a nice payoff application in terms of an introduction to quantum mechanics.

May be my only complaint was that the exercises seemed mostly five-finger ones. With that said, they should still challenge an undergraduate or beginning graduate, if not force them to re-visit the definitions and basic methods of proof.

I've always thought Rudin's "Mathematical Analysis" book deserved the title of "Best Undergraduate Math Text Ever", but this book has made me rethink that position.

5-0 out of 5 stars The definition of classic
As shown in the first line on the cover:
Wiley CLASSICS Library

5-0 out of 5 stars Possibly the BEST math book that I have ever read
The presentation of concepts, definitions, and proofs are clear and EASILY understandable!The problems are illustrative and reinforce one's understanding of the material.I am in the middle of a class in functional analysis.It is a JOY to use this book.If you are interested in functional analysis and can't take a class in the subject, this book should prove to be sufficient by itself.It is that good!I cannot speak highly enough about this great book! ... Read more

Isbn: 0471504599
Sales Rank: 149780
Subjects:  1. Applied    2. Calculus    3. Functional Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / Applied    7. Numerical analysis   


$71.95

Functional Analysis
by WalterRudin
Average Customer Review: 4.5 out of 5 stars
Hardcover (01 January, 1991)
list price: $131.56 -- our price: $131.56
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Reviews (4)

3-0 out of 5 stars Decent book, if you can get it cheap
I strongly urge any serious math student to own a copy of both Rudin's Principles ("Baby Rudin") and his Real and Complex Analysis ("Adult Rudin").The former is absolutely essential- without completely mastering continuity and convergence on the basic metric space topology on R^n, higher math is going to be quite a pain.The second is good because it puts the major ideas of basic analysis- Radon measures, L^p spaces, rudiments of Hilbert and Banach Spaces, differentiation and integration, Fourier and Harmonic Analysis, Holomorphic and meromorphic functions, etc. all in one nice volume, although the problems may be too challenging or tangential to master the material by doing them.

With that said, I don't like this book as much.Perhaps because the problems don't provide great movitation for the theorems- in any event, I would recommend using at least two books to understand functional analysis.One that emphasizes a rigorous approach to the theory involved, and another more applied book that allows you to play with the new tools to solve the problems functional analysis was invented to solve; quantum mechanics, for example.

Reed and Simon is a good book, although I'm sure physicists or physics students would probably complain about it for the same reason I like it- its very mathematically rigorous and has a ton of problems- 30 to 60 on average at the end of each chapter, with only a few digressions into applications into quantum physics or elementary QFT.Get this with some Springer text, like Elements of Functional Analysis.

One more note- Rudin's book is broken up into three parts- one on TVS (Topological vector spaces) that combines topological properties of a space (for example, local convexity or local compactness) with the usual vector-space operations to set the spaces where operators act.

The second section deals with distributions- I regret that one failure of "Adult Rudin" was to emphasize the abstract integral as a linear functional, because this would have helped to make the concept of a distribution more clear.

While the introduction to distributions and their connections to Fourier analysis and differential equations is nice, the text gets bogged down with proofs about convolutions that are highly technical (and make either good practice or a good time for Rudin to actually use, for once, "The details are left to the reader...").

Finally, Rudin introduces operator theory, although it could go much more smoothly- the proofs come off as way too technical, a far cry from the "slickness" his proofs are often accused of being in the graduate analysis text.

All in all, there's some interesting problems to do, but you're not going to understand the applications of Functional Analysis to quantum mechanics or PDE (other than distributions a little), where other, more applied (read: easier) books may give nice problems about applications of Hilbert space methods, such as variational techniques or Fredholm theory.

5-0 out of 5 stars Modern topics in math.
"Modern analysis" used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less "modern". The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability
to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has the AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitated interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.

5-0 out of 5 stars The Bible on Distributions
No other book covers the elements of distributions and the fourier transform quite like Rudin's Functional Analysis.This is a must for every budding PDE-er! ... Read more

Isbn: 0070542368
Sales Rank: 204987
Subjects:  1. Advanced    2. Functional Analysis    3. Mathematics    4. Science/Mathematics    5. Mathematics / Functional Analysis   


$131.56

Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
by Peter D.Lax
Average Customer Review: 5.0 out of 5 stars
Hardcover (22 March, 2002)
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Reviews (2)

5-0 out of 5 stars Excellent
Peter D Lax is one of the great mathematicians of the 2nd half of the 20th century. Buy this book if only to have it on your bookshelf. After a long day of suffering fools and putting up with the latest insanities of your university administrators, leaf through Lax's book to recover. This is mathematics at its best. What better use can we put mathematics to, than to help us regain our sanity in a world that's gone mad.

5-0 out of 5 stars Brings the subject to life!
The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with
seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. It gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for

quantum theory, for dynamical systems, and for partial differential equations. The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor
in theories surprisingly far from the original roots of the subject. Peter Lax has himself,-- alone and with others, shaped some ofgreatest successes of the period, right up to the present. That is in the book!! And it offers an upbeat outlook for the future. It has been tested in the class room,-it is really user-friendly. At the end of each chapter P Lax ofers personal recollections;-- little known stories of how several of the pioneers in the subject have been victims,- in the 30ties and the 40ties, of Nazi atrocities. The writing is crisp and engaged,- the exercises are great;- just
right for students to learn from. This is the book to teach from. ... Read more

Isbn: 0471556041
Sales Rank: 120701
Subjects:  1. Functional Analysis    2. Mathematics    3. Science/Mathematics    4. Mathematics / Functional Analysis   


$91.71

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